Ok, here are some preliminary results. First of all, here are the m-files used:
http://sites.google.com/site/theckhd/mf ... avoid_dr.m http://sites.google.com/site/theckhd/mfiles/avoid_dr.m http://sites.google.com/site/theckhd/mf ... d_inc_dr.m The calc file contains all of the logic for the investigation. avoid_dr is a utility function that calculates net avoidance after diminishing returns, and avoid_inc_dr is a utility function that determines how much avoidance one gains from 8 rating points of dodge, parry, defense, or agility for a particular set of input values.
First, let's look at the raw diminishing returns progression. For this we'll assume we start with a base of 0 of any rating or stat from gear. We just want to know how each rating is affected by the diminishing returns function.
As you can see, Defense Rating is least affected by DR, followed by dodge. Agility is only about 80% effective point for point towards dodge rating, as expected. Parry and Agility switch places after around 885 parry rating. We can replot these results so that instead of total avoidance, we see the amount of avoidance per 8 ipoints (i.e. a rare quality gem with 8 dodge, parry, or defense rating or 8 agility):
Again, the results are basically unchanged, though the crossover for agility and parry is lower here (at around 380). This makes perfect sense, by the way; the last graph was telling us that 885 parry gives the same amount of avoidance as 885 agility. If parry starts out better, it obviously has to get worse per point much earlier than 885 so that agility can catch up.
Of course, neither of these graphs tell us anything particularly interesting. We already knew parry had harsher diminishing returns than dodge, and each of these plots is taken in a vacuum - in other words, with 0 of each of the other ratings. This is a terrible assumption right out of the starting gate, since a tank is going to gear for 689 defense before he even starts worrying about dodge or parry.
As a first approximation, let's assume that we're starting with 689 defense from gear, and re-run the calculation for each additional point of rating:
The addition of crit-immunity changes things considerably. Now Dodge is the clear winner initially, and parry is already lagging behind. Again though, the story this tells us is rather limited. According to this, if we add about 160 dodge rating, another 8 points of dodge rating will be roughly equivalent to 8 points of defense. But of course, that 160 dodge rating has already decreased the value of the dodge contribution from defense, so the comparison isn't strictly valid! Compounding this, we're completely ignoring the dodge we'd be getting from agility buffs.
The inherent problem here is how intertwined dodge, defense, and parry are. Increasing any one directly affects the value of at least one of the others. This makes it very difficult to try and isolate one and examine it. If we were only interested in two things (say dodge and parry), we could make a 3-dimensional mesh or surface plot that would tell us the optimum ratio of those two stats as either increases. This would work fine for just dodge or parry, but to include defense we'd need to go to a 4-dimensional plot, which is much harder to analyze.
Instead, let's take a different approach. Starting from our base assumption of 689 defense and no other stats from gear, we can calculate which stat gives us the biggest avoidance boost from 8 points of rating. The previous plot has already shown us this will be dodge, so for our first iteration, we'll add 8 dodge rating to our gear set. Now we have 8 dodge rating, 0 parry rating, 689 defense rating, and 0 Agility. I'm going to ignore Agility for the moment, since it will always be strictly inferior to dodge for raw avoidance - we'll leave the EH benefits of Agility for another discussion.
We'll then re-run the DR formulas to see which stat is best, and repeat the process. If our next iteration shows parry as better, we add 8 parry rating, and so forth. We repeat this until we find the point where all three are giving roughly the same amount of avoidance. For the first 70 iterations, this is what the plot looks like:
We see that the noticeable lead dodge had in the earlier plots manifests itself here. We end up adding only dodge rating for the first 30 iterations, for a total of 232 dodge rating. The bottom plot shows that this is the point where Dodge and Parry are both giving nearly identical contributions. We'll keep a running tally so we can see where this is going:
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Iteration Dodge Defense Parry
0 0 689 0
30 232 689 0
On iteration 31, we start adding parry rating as well. We see that we only add dodge and parry in a 1.75:1 ratio until iteration 53, where we see our first 8 points of defense. It's a little hard to see from the bottom plot this time, but that's exactly where DR brings dodge and parry down to the same level as defense. At iteration 52, we have 344 dodge rating and 64 parry rating. In percentages, that's 11.94% dodge and 6.3% parry from gear (also 4.29% miss from the defense).
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Iteration Dodge Defense Parry
0 0 689 0
30 232 689 0
52 344 689 64
To continue any further, we need to run the simulation for more iterations. Here's the result for 500 iterations:
It's harder to see what's going on at the beginning here, but we very clearly have what looks like a linear progression for each stat with different slopes corresponding to their relative amounts. The bottom plot also clearly shows all three adding almost identical amounts of avoidance per 8 rating, indicating that the simulation is working properly.
If we take the values out at 500 iterations, and subtract off the values at around 100 iterations, we can calculate the ratios in which we want to add the values. Between iteration 100 and 500, we've added 1496 dodge rating, 1096 defense rating, and 608 parry rating, for a ratio of
2.46 : 1.80 : 1 dodge : defense : parry.
Let's see how sensitive this is to initial conditions. Remember how we ignored the fact that when we're raid-buffed, we'll have some dodge from Agility? Let's add that into the mix. This time, we'll start with 300 agility from buffs and 689 defense rating. The plot and table then look like this:
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Iteration Dodge Defense Parry
0 0 689 0
3 0 689 16
21 96 689 64
This time parry is the best initially, at least briefly, and then parry and doge are added in a 3:2 ratio until we hit the point where defense enters the mix. This works out to 11.96% dodge and 6.35% parry, very close to the numbers we found before. As expected, the agility just takes the place of some of the dodge rating we had to add in the first example. The ratio we get this time is
2.45 : 1.82 : 1 dodge : defense : parry, very similar to the last calculation.
Assuming we get 10% dodge and parry from base+talents, and 1.65% dodge from our 90 base agility at level 80, that means that the ideal gearing progression would be to:
- Add dodge and parry until we reach around 23.6% dodge and 16.35% parry fully raid buffed (96 dodge rating, 64 parry rating, or 11.96% dodge and 6.35% parry from gear alone)
- Add dodge, defense, and parry rating in a 2.4 : 1.8 : 1 ratio.
